Question

$C_1$ is a circle with centre at the origin and radius equal to $r$ and $C_2$ is a circle with centre at $(3r,0)$ and radius equal to $2r$. The number of common tangents that can be drawn to the two circles are

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is C $3$

As per the figure, the smaller circle $C_1$ of radius $r$ passes through the points $(-r,0)$ and $(r,0)$ on $x$ axis.

And the circle $C_2$ passes through the points $(r,0)$ and $(5r,0)$ on $x$ axis.

Thus, the circles touch each other externally.

Therefore, three common tangents are possible between them, one perpendicular to $x$ axis, passing through the common point $(r,0).$

The other two, being symmetric about the x axis and touching both the circles.